2002
DOI: 10.1063/1.1482156
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Reconstruction of Abel-transformable images: The Gaussian basis-set expansion Abel transform method

Abstract: In this article we present a new method for reconstructing three-dimensional ͑3D͒ images with cylindrical symmetry from their two-dimensional projections. The method is based on expanding the projection in a basis set of functions that are analytical projections of known well-behaved functions. The original 3D image can then be reconstructed as a linear combination of these well-behaved functions, which have a Gaussian-like shape, with the same expansion coefficients as the projection. In the process of findin… Show more

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Cited by 866 publications
(739 citation statements)
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References 17 publications
(16 reference statements)
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“…Each image is used to reconstruct a three-dimensional scattering distribution using an inverse Abel transformation. 39 The speed distributions, P Cl (V), of the Cl fragments are extracted by integrating the threedimensional velocity distributions over all solid angles at each speed. Using momentum conservation and the appropriate Jacobian, the center of mass recoil translational energy distributions P(E T ) from the photodissociation are derived from the Cl speed distributions.…”
Section: Resultsmentioning
confidence: 99%
“…Each image is used to reconstruct a three-dimensional scattering distribution using an inverse Abel transformation. 39 The speed distributions, P Cl (V), of the Cl fragments are extracted by integrating the threedimensional velocity distributions over all solid angles at each speed. Using momentum conservation and the appropriate Jacobian, the center of mass recoil translational energy distributions P(E T ) from the photodissociation are derived from the Cl speed distributions.…”
Section: Resultsmentioning
confidence: 99%
“…21 The Integrated photoelectron images are symmetrized to account for detector inhomogeneities and converted into three-dimensional momentum distributions by standard methods. 22 From these, photoelectron kinetic energy (eKE) and angular distributions are readily obtained. In many of the spectra shown here, one observes broad features with maximum intensity at kinetic energy eKE max ; these features are characterized by their vertical detachment energy, VDE, defined by VDE ) hν probe -eKE max .…”
Section: Methodsmentioning
confidence: 99%
“…The positions of photoelectrons were recorded by a charge-coupled device (CCD) camera and one image data was obtained by accumulating 50000−100000 laser shots. The original 3D distribution was reconstructed using the Basis Set Expansion (BASEX) inverse Abel transform method, 50 and the photoelectron spectrum and the anisotropy parameters of transition bands were acquired by calculations based on one central slice of the 3D distribution. The spectrometer was calibrated using the spectra of Ag − and Au − at 355 nm.…”
Section: Methodsmentioning
confidence: 99%